Fast and Flexible Emulation of Spatial Extremes Processes via Variational Autoencoders

Many real-world processes have complex tail dependence structures that cannot be adequately characterized using classical Gaussian processes. Alternatively, models motivated by extreme-value theory exhibit appealing extremal dependence properties but are often exceedingly prohibitive to fit and simulate from in high dimensions using classical methods. In this article, we extend the boundaries on computation and modeling of high-dimensional spatial extremes by integrating a new flexible and nonstationary spatial extremes model into the encoding-decoding structure of a variational autoencoder, called the extremes variational autoencoder (XVAE). Our proposed model is not only able to capture asymptotic dependence and independence, but also spatio-temporal heterogeneity in its tail behavior. The proposed XVAE is designed to realistically emulate spatial observations and produce outputs that have similar statistical properties as the inputs, especially in the tail. By exploiting our neural-network-based approach, we also provide a novel way of making fast inference with complex extreme-value processes. Through extensive simulation studies, we show that the XVAE is substantially more time-efficient than traditional Bayesian inference methods and outperforms other competing modeling approaches. Lastly, we analyze a high-resolution satellite-derived dataset of sea surface temperature in the Red Sea, which includes 30 years of daily measurements at 16,703 grid cells. We demonstrate how the XVAE can be used to identify regions susceptible to marine heatwaves and how these have evolved during the study period. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.